Large complex networks frequently exhibit recurring subgraph patterns that can provide valuable insights into the organization of the underlying network structure. In histopathology, cell nuclei can be used for the construction of a cell graph (CG) that characterizes localized tissue architecture by constructing a series of disconnected subgraphs on an image. Conventional approaches to the quantification of subgraph similarity have traditionally relied on graph matching techniques that define graph matching and similarity as correspondence issues. However, the unstable and polynomial nature of conventional graph matching techniques makes them unsuitable for the analysis of large histopathology images that require computationally expensive explicit comparison of thousands of graphs. Conventional methods also fail to compare populations of subgraphs between various images that are decomposed via a CG into series of subgraphs.
Variations of tumor morphology relate to prognosis and patient outcomes. The primary means of diagnosing most cancers is histopathological examination of biopsy tissue to create a diagnostic profile based on cell morphology, cytoplasmic changes, cell density, and cell distribution. Visual characterization of tumor morphology via grading is, however, time consuming, highly subjective, and suffers from high inter-rater and intra-rater variability. Conventional visual grading of tumor morphology by a human pathologist may therefore be less than optimal in clinical situations where timely and accurate classification can affect patient outcomes.
Graph theory can be used to characterize the structure of large networks leading to improved understanding of dynamic interactions and patterns that exist between components of the network. Nodes with similar characteristics tend to cluster together forming sub-structures within the network. Sub-structures may be represented as subgraphs. Despite their complex nature, cancerous cells tend to self-organize in clusters and exhibit architectural organization.
Large networks often include subgraphs that provide valuable information on the interactions of nodes at a local level. Conventional methods that employ Voronoi (VT) graphs and Delaunay (DT) graphs may have biological context and potentially predict disease severity. However, conventional methods that employ VT graphs and DT graphs are limited to estimating global statistics. Conventional techniques and cell graphs may decompose an image into subgraphs by using clusters of nuclei as nodes, but do not identify similar subgraph structures that may recur across a population. Additionally, conventional approaches do not capture the effect of similar subgraph structures on overall tumor morphology.